The river flows 45º N of E, so its velocity vector is
w = (7.1 m/s) (cos(45º) i + sin(45º) j) ≈ (5.02 m/s) (i + j)
The boat captain wants to move against the current such that the boat moves due E, so that the resultant is
r = (19.74 m/s) cos(0º) i = (19.74 m/s) i
The boat's speed in still water is 13 m/s, and should be moved in a direction θ such that the boat's velocity will be
b = (13 m/s) (cos(θ) i + sin(θ) j)
We need to have
w + b = r
Match up the components and solve for θ :
5.02 m/s + (13 m/s) cos(θ) = 19.74 m/s
5.02 m/s + (13 m/s) sin(θ) = 0
cos(θ) ≈ 1.13
sin(θ) ≈ -0.386
tan(θ) = sin(θ) / cos(θ) ≈ -0.341
θ ≈ -18.8º
So the captain should point the boat 18.8º S of E.
